Question: Simplify the following expression: $p = \dfrac{-42y}{30y^2 + 60y}$ You can assume $y \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-42y = - (2\cdot3\cdot7 \cdot y)$ The denominator can be factored: $30y^2 + 60y = (2\cdot3\cdot5 \cdot y \cdot y) + (2\cdot2\cdot3\cdot5 \cdot y)$ The greatest common factor of all the terms is $6y$ Factoring out $6y$ gives us: $p = \dfrac{(6y)(-7)}{(6y)(5y + 10)}$ Dividing both the numerator and denominator by $6y$ gives: $p = \dfrac{-7}{5y + 10}$